Question

If \(z_1\) and \(z_2\) be two roots of the equation \(z^2 + az + b = 0, \, a^2 < 4b\), then the origin, \(z_1\) and \(z_2\) form an equilateral triangle if:

• A. \(a^2 = 3b^2\)
• B. \(a^2 = 3b\)
• C. \(b^2 = 3a\)
• D. \(a^2 = b^2\)

Hint:

When roots form geometric shapes such as equilateral triangles, use geometric properties and the relation between the coefficients of the quadratic equation to derive the required conditions.